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A multi-scale framework is proposed for the prediction of the macroscopic hygro-elastic properties of oak wood. The distinctive features of the current multi-scale approach are that: (i) Four different scales of observation are considered, which enables the inclusion of heterogeneous effects from the nano-, micro-, and meso-scales in the effective constitutive behavior of oak at the macro-scale, (ii) the model relies on three-dimensional material descriptions at each considered length scale, and (iii) a moisture-dependent constitutive assumption is adopted at the nano-scale, which allows for recovering the moisture dependency of the material response at higher scales of observation. In the modeling approach, oak wood is assumed as homogeneous at the macro-scale. The meso-scale description considers the cellular structure of individual growth rings with three different densities. At the micro-scale, the heterogeneous nature of cell walls is described by the characteristics of the primary and secondary cell wall layers. Finally, the nano-scale response is determined by cellulose micro-fibrils embedded in a matrix of hemicellulose and lignin. The oak properties at the four length scales are connected via a three-level homogenization procedure, for which, depending on the geometry of the fine-scale configuration, an asymptotic homogenization procedure or Voigt averaging procedure is applied at each level to determine the effective hygro-elastic properties at the corresponding coarse scale. In addition, the moisture adsorption isotherms at each scale are constructed from a volume-weighted averaging of the moisture adsorption characteristics at the scale below. The computational results demonstrate that the macro-scale moisture-dependent, hygro-elastic behavior of oak wood is predicted realistically, thereby revealing the influence of the material density, the micro-fibril orientation, and the hygro-elastic properties from the underlying scales. The computed macro-scale properties of oak are in good agreement with experimental data reported in the literature. [ABSTRACT FROM AUTHOR]

The hygro-thermo-expansive response of fibrous networks involves deformation phenomena at multiple length scales. The moisture or temperature induced expansion of individual fibres is transmitted in the network through the inter-fibre bonds; particularly in the case of anisotropic fibres, this substantially influences the resulting overall deformation. This paper presents a methodology to predict the effective properties of bonded fibrous networks. The distinctive features of the work are i) the focus on the hygro-thermo-mechanical response, whereas in the literature generally only the mechanical properties are addressed; ii) the adoption of asymptotic homogenization to model fibrous networks. Asymptotic homogenization is an efficient and versatile multi-scale technique that allows to obtain within a rigorous setting the effective material response, even for complex micro-structural geometries. The fibrous networks considered in this investigation are generated by random deposition of the fibres within a planar region according to an orientation probability density function. Most of the available network descriptions model the fibres essentially as uni-axial elements, thereby not explicitly considering the role of the bonds. In this paper, the fibres are treated as two dimensional ribbon-like elements; this allows to naturally include the contribution of the bonding regions to the effective expansion. The efficacy of the proposed study is illustrated by investigating the effective response for several network realizations, incorporating the influence of different micro-scale parameters, such as fibre hygro-thermo-elastic properties, orientation, geometry, areal coverage. [ABSTRACT FROM AUTHOR]

This paper presents a multi-scale approach to predict the effective hygro-mechanical behaviour of paper sheets based on the properties of the underlying fibrous network. Despite the vast amount of literature on paper hygro-expansion, the functional dependence of the effective material properties on the micro-structural features remains yet unclear. In this work, a micro-structural model of the paper fibrous network is first developed by random deposition of the fibres within a planar region according to an orientation probability density function. Asymptotic homogenization is used to determine its effective properties numerically. Alternatively, two much more idealized micro-structural models are considered, one based on a periodic lattice structure with a regular network of perpendicular fibres and one based on the Voigt average. Despite their simplicity, they reproduce representative micro-structural features, such as the orientation anisotropy and network level hygro-elastic properties. These alternative models can be solved analytically, providing closed-form expressions that explicitly reveal the influence of the individual micro-scale parameters on the effective hygro-mechanical response. The trend predicted by the random network model is captured reasonably well by the two idealized models. The resulting hygro-mechanical properties are finally compared with experimental data reported in the literature, revealing an adequate quantitative agreement. [ABSTRACT FROM AUTHOR]

This paper proposes a meso-structural model for the discrete fibrous network of paper, which is able to upscale the irreversible phenomena from the underlying hygro-mechanics towards the effective behaviour at the macro-scale. The swelling of individual fibres, induced by moisture content variations, is transmitted to the network through inter-fibre bonds and governs the resulting effective material response. The present approach is based on a recently developed discrete meso-structural model for the reversible part of the response, which distinguishes between the influence on the hygroscopic behaviour of free-standing fibre segments and inter-fibre bonds. The network structure, fibre and bond geometries and hygro-elastic properties are explicitly incorporated. The major novelty of this contribution is the extended fibre constitutive model, enabling to describe some typical irreversible mechanisms and instability effects related to the history of the manufacturing. This extension strongly affects the effective material behaviour beyond the elastic range. Despite the valuable work in the literature, no papers can be found dedicated to meso-structural models including these phenomena. Using an appropriate homogenization strategy, the unit-cell is solved analytically, capturing irreversible shrinkage in restrained dried paper and the occurrence of local buckling within the bond for freely dried material. The proposed scale transition offers a deeper insight into the complex relation between the events occurring at the different length scales. The potential of the proposed methodology is demonstrated through the convincing agreement with experimental data obtained from the literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a continuous-discontinuous computational homogenization-localization framework to upscale microscale localization toward the onset and propagation of a cohesive discontinuity at the macroscale. The major novelty of this contribution is the development of a fully coupled micro-macro solution strategy, where the solution procedure for the macroscopic domain is based on the extended finite element method. The proposed approach departs from classical computational homogenization, which allows to derive the effective stress-strain response before the onset of localization. Upon strain localization, the microscale is characterized by a strain localization band where damage grows and by two adjacent unloading bulk regions at each side of the localization zone. The microscale localization band is lumped into a macroscopic cohesive crack, accommodated through discontinuity enriched macroscale kinematics. The governing response of the continuum with a discontinuity is obtained numerically based on proper scale transition relations in terms of the traction-separation law and the stress-strain description of the continuous surrounding material at both sides of the discontinuity. The potential of the method is demonstrated with a numerical example, which illustrates the onset and propagation of a macroscale cohesive crack emerging from microstructural damage within the underlying microstructure. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the present contribution, the effective mechanical, diffusive, and chemo-expansive properties of concrete are computed from a multi-scale and multi-physics approach. The distinctive features of the approach are that i) the mechanical and diffusive responses are modelled in a coupled fashion (instead of separately, as is usually done), and that ii) the multi-scale model considers three different scales of observation, which allows for including heterogeneous effects from both the micro- and meso-scales in the effective macro-scale properties of concrete. At the macro-scale, the concrete material is considered as homogeneous, whereas at the meso-scale it consists of particle aggregates embedded in a porous cement paste. At the micro-scale the porous cement paste is described as a two-phase material, composed of a solid cement phase and saturated capillary pores. Adopting a two-level asymptotic homogenization procedure, the effective meso-scale properties of the porous cement paste are computed first, using a unit cell that includes the cement paste and pore characteristics. Subsequently, the obtained meso-scale response of the porous cement paste, together with the aggregate characteristics, defines the material properties of a second unit cell, which is used for calculating the effective macro-scale response of concrete. The distributions of the pores and the aggregates within the unit cells are determined from a uniform, random distribution of points, and their radii are defined from a probability distribution function. The efficacy of the proposed framework is illustrated by studying the effective mesoscopic response of a porous cement paste, which demonstrates the influence of the micro-scale porosity and pore percolation. Next, the effective macroscopic response of concrete is analysed, by considering the influence of the aggregate volume fraction, the mismatches in elastic stiffnesses and diffusivity between the aggregate and the cement paste, and the porosity. The computed effective properties are compared with experimental data from the literature, showing a good agreement. [ABSTRACT FROM AUTHOR]